Let the number of history textbooks be h and the number of physics textbooks be p.
It was given that the bookstore sells a combined total of 347 books. Thus we have:
[tex]h+p=347[/tex]It is also given that the number of history textbooks sold was 79 more than the number of physics textbooks. This gives:
[tex]h=p+79[/tex]We can substitute for h into the first equation:
[tex]p+79+p=347[/tex]Solving, we have:
[tex]\begin{gathered} 2p+79=347 \\ 2p=347-79 \\ 2p=268 \\ p=\frac{268}{2} \\ p=134 \end{gathered}[/tex]Substitute for p in the second equation, we have:
[tex]\begin{gathered} h=p+79 \\ h=134+79 \\ h=213 \end{gathered}[/tex]Therefore, there were 134 physics textbooks and 213 history textbooks.
What is 2902 divided by 3
Answer:
967.333333
Step-by-step explanation:
If you need to round it, it's 967.33
As a fraction, it's 2902/3 or 967 1/3
write the equation of the line parallel to y = -5x + 3 with a y - intercept (0,4).
Equation of the line
The equation of a line can be expressed in slope-intercept form as follows:
y = mx + b
Where m is the slope of the line and b is the y-intercept.
We are given the equation of a line:
y = -5x + 3
This line as a slope of m=-5 and the intercept with the y-axis is y=3
We are required to find the equation of another line that is parallel to the given line. Parallel lines have the same slope. Thus the slope of our new line is also m=-5.
We are also given the y-intercept of the new line (0,4). This means the value of b is 4.
Knowing the values of m and b, we can write the equation of the required line as:
y = -5x + 4
A straight line passes through points (1, 15) and(5, 3) What isthe equation of the line?Select one:A) y = - 3x + 18B) y = – 7x + 18C) y = 2x + 18D) y = 3x + 18
Points (1,15) and (5,3)
Find the slope (m)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where:
(x1,y1) = (1,15)
(x2,y2) = (5,3)
Replacing:
[tex]m=\frac{3-15}{5-1}=\frac{-12}{4}=-3[/tex]the function has a slope m= -3
slope intercept form:
y=mx+b
Where
m= slope
so, the correct function is
y=-3x+18 (A)
Evaluate. Express your answer in scientific notation. 7.94 x 10^-3 6.69 x 10^-4
To solve this question, follow the steps below.
Step 01: Write the numbers to have the same powers.
To do it, choose one number to transform.
Let's choose the number with the greaters power (10⁻³).
To write it with the power -4, multiply 7.94 by 10:
[tex]\begin{gathered} 7.94\times10^{-3}=7.94\operatorname{\times}10*10^{-4} \\ =79.4\operatorname{\times}10^{-4} \end{gathered}[/tex]Step 02: Solve the subtraction.
To solve the subtraction, subtract the decimals.
[tex]\begin{gathered} 79.4\operatorname{\times}10^{-4}-6.69\operatorname{\times}10^{-4} \\ =(79.4-6.69)\operatorname{\times}10^{-4} \\ =72.71\operatorname{\times}10^{-4} \end{gathered}[/tex]Step 03: Rewrite the number in scientific notation.
For a number in scientic notation a x 10ᵇ, 1 ≤ |a| < 10.
Then, divide 72.71 by 10 and multiply the exponent part by 10.
[tex]\begin{gathered} \frac{72.71}{10}\times10^{-4}\times10 \\ 7.271\times10^{-4+1} \\ 7.271\times10^{-3} \end{gathered}[/tex]Answer:
[tex]7.271\cdot10^{-3}[/tex]
Amy and Fraser walk inside a circular lawn. Point O is the center of the lawn, as shown below:
Answer
Amy walks a distance equal to the diameter, and Frasier walks a distance equal to the radius of the lawn
Step-by-step explanation
Segment BC represents the diameter of the circle (a segment that connects two points on the circle and it passes through the center of the circle).
Segment OA represents the radius of the circle (a segment that connects the center of the circle and a point on the circle)
How to solve Use completing the square to find the vertex of the following parabolas
To use completing the square to find the vertex of the given parabola, we proceed as follows:
[tex]g(x)=x^2-5x+14[/tex]- we divide the coefficient of x by 2 and add and subtract the square of the result, as follows:
[tex]g(x)=x^2-5x+(\frac{5}{2})^2-(\frac{5}{2})^2+14[/tex]- simplify the expression as follows:
[tex]\begin{gathered} g(x)=(x^2-5x+(\frac{5}{2})^2)-(\frac{5}{2})^2+14 \\ \end{gathered}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-(\frac{5}{2})^2+14[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-\frac{25}{4}^{}+14[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2-\frac{25}{4}^{}+\frac{56}{4}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{-25+56}{4}^{}[/tex][tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{31}{4}^{}[/tex]From the general vertex equation, given as:
[tex]g(x)=a(x-h)^2+k[/tex]The coordinate of the vertex is taken as: (h, k)
Therefore, given:
[tex]g(x)=(x^{}-\frac{5}{2})^2+\frac{31}{4}^{}[/tex]We have the vertex to be:
[tex](\frac{5}{2},\frac{31}{4})\text{ or (2.5, 7.75)}[/tex]Find the area of the region enclosed by y = 7x and y = 8x^2.
Solution
Hence the area under the region is
[tex]A=\int_0^{0.875}7x-8x^2=\frac{343}{384}unit^2[/tex]The units of the subway map below are in miles. Suppose the routes between stations are straight. Find the approximate distance a passenger would travel between stations J and K.
Point J has coordinates (2,6)
Point K has coordinates (-1,-3)
The distance between 2 point is given by
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]where
[tex]\begin{gathered} (x_1,y_1)=\mleft(2,6\mright) \\ (x_2,y_2)=(-1,-3) \end{gathered}[/tex]By substituying these values, we have
[tex]\begin{gathered} d=\sqrt[]{(-1_{}-2)^2+(-3-6)^2} \\ d=\sqrt[]{(-3)^2+(-9)^2} \\ d=\sqrt[]{9+81} \\ d=\sqrt[]{90} \end{gathered}[/tex]hence,
[tex]d=9.49[/tex]A bag contains the following marbles: 12 black marbles, 8 blue marbles, 16 brown marbles and 14 green marbles. what is the ratio of black marbles to blue marbles.
Let:
Nbk = Number of black marbles = 12
Nb = Number of blue marbles = 8
The ratio of black marbles to blue marbles will be given by:
[tex]Nbk\colon Nb=12\colon8=\frac{12}{8}=\frac{3}{2}[/tex]Hello. I’ve attached a photo thank you Find Are and Perimeter.
Given:
Base of the parallelogram, b = 8
Height of the parallelogram, h = 3
Side of the parallelogram, a = 4
Required: Area and Perimeter
Explanation:
The formula to find the area of a parallelogram is
[tex]A=bh[/tex]where b is the base and h is the height.
Plug the given values into the formula.
[tex]\begin{gathered} A=8\cdot3 \\ =24 \end{gathered}[/tex]The formula to find the perimeter is
[tex]P=2a+2b[/tex]Plug the given values into the formula.
[tex]\begin{gathered} P=2\cdot4+2\cdot8 \\ =8+16 \\ =24 \end{gathered}[/tex]Final Answer: Area = 24, Perimeter = 24
1. The diagram below, not drawn to scale, shows a flexible piece of paper in the shape of a sector of a circle with centre 0 and radius 15 cm. 22 Use . B А 126 0 15 cm C (a) Show that the perimeter of the paper is 63 cm. [3] (b) Calculate the area of the paper OABC. 121 (c) The paper is bent and the edges OA and OC are taped together so that the paper forms the curved surface of a cone with a circular base, ABC. (1) Draw a diagram of the cone formed, showing clearly the measurement 15 cm, the perpendicular height, h, and the radius, r, of the base of the cone. [1] (ii) Calculate the radius of the circular base of the cone. 121 (iii) Using Pythagoras' Theorem, or otherwise, determine the perpendicular height of the resulting cone. 121
Given
Circle of radius 15 cm and angle at the centre equal to 126 degree.
Find
(a) Perimeter of the paper is 63cm.
(b) Area of the paper OABC
(c) i) Draw a cone
ii) radius of circular base
iii) determine the height
Explanation
(a)
Perimeter of sector = Arc length ABC + AO + OC
Arc Length of ABC =
[tex]\begin{gathered} \frac{\theta}{360}\times2\Pi r \\ \frac{126}{360}\times2\times\frac{22}{7}\times15 \\ 33 \end{gathered}[/tex]so , perimeter = 33 +15 +15 = 63
Hence we proved that perimeter is 63 cm
(b) Area of sector =
[tex]\begin{gathered} \frac{\theta}{360}\times\Pi r^2 \\ \frac{126}{360}\times\frac{22}{7}\times15\times15 \\ 247.5 \end{gathered}[/tex](c) i)
ii) Circumference of base =
[tex]\begin{gathered} 2\Pi r=\text{33} \\ r=\frac{33\times7}{2\times22} \\ r=\frac{21}{4} \end{gathered}[/tex]iii) l = 15 cm, r= 21/7
By pythagoras theorem,
[tex]\begin{gathered} h^2=l^2-r^2 \\ h^2=15^2-(\frac{21}{4})^2 \\ h=\text{ 14.05} \end{gathered}[/tex]Final Answer
(a) 63
(b) 247.5
W XZWhich statement regarding the diagram is true?O mzWXY = mzYXZO mzWXY
Linear pair of angles are formed when two lines intersect each other at a single point.
The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.
The figure shows the line WZ intersected by lines YX and YZ. At X, two adjacent angles are formed at the point where WZ and YX intersect.
This means angles WXY and YXZ are linear angles.
Linear angles always add up to 180°, thus:
m∠WXY + m∠YXZ = 180°
A junk drawer at home contains eight pens four of which work what is the probability that a randomly grab three pens from the drawer and don’t end up with a pen that works express your answer as a fraction in lowest terms or decimal rounded to the nearest million
Answer:
1/14
Explanation:
The number of ways or combinations in which we can select x objects from a group of n can be calculated as:
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]So, if we are going to select 3 pens from the drawer that contains 8 pens, the number of possibilities is:
[tex]8C3=\frac{8!}{3!(8-3)!}=\frac{8!}{3!\cdot5!^{}}=56[/tex]Then, if we didn't end up with a pen that works is because we select the three pens from the 4 that didn't work. In this case, the number of possibilities is:
[tex]4C3=\frac{4!}{3!(4-3)!}=\frac{4!}{3!\cdot1!}=4[/tex]Therefore, the probability required is equal to the ratio of these quantities:
[tex]P=\frac{4}{56}=\frac{1}{14}[/tex]So, the answer is 1/14
A dilation from the origin with scale factor of 3 will map the point (5,4) to (8,7) explain why or why not this statement is correct
This statement is false because if the factor of dilatation is 3, the new coordinates should be 3 times the original ones. So the new point shoud be (15,12)
Which equation describes the relationship between the tangent and the secant line segments?
Answer:
B. (PQ)² = (PR)(PS)
Step-by-step explanation:
You want the relationship between tangent PQ and the segments of secant PS.
Secant relationThe product of the secant lengths between the point P where it meets the tangent and the two point R and S where it intersects the circle is equal to the square of the tangent from point P.
The relationship is ...
(PQ)² = (PR)(PS)
__
Additional comment
You can eliminate choices C and D because they do not involve segments of PS.
If M is the midpoint of RS, choice A says PQ=PM. Actually PQ < PM, which is clear when RS is a diameter of the circle. This leaves only choice B.
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a ladder 15 feet long leans against a house and make a angle of 60 degrees with the ground . find the distance from the house to the foot of the ladder .
We can use the next diagram in order to solve the question
we need to find x, x is the distance from the house to the foot of the ladder, we will use a trigonometric function in order to find x in this case we will use the cosine
[tex]\cos (\theta)=\frac{AS}{H}[/tex]where
θ= 60°
AS=x
H=15 ft
we substitute the values
[tex]\cos (60)=\frac{x}{15}[/tex]we need to isolate the x
[tex]x=\cos (60)(15)=7.5ft[/tex]the distance from the house to the foot of the ladder is 7.5 ft
Graph the parabola.y=-4x² +5Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button
This is the basic parabola shifted 5 units up.
So, the vertex is at::
(0, 5)
Now, to get 2 points to the left, we take x = -1 and x = -2 and find corresponding y value.
To get 2 points to the right, we take x = 1 and x = 2 and find corresponding y values.
Thus,
When x = -1,
y = -4(-1)^2 + 5
y = 1
When x = -2,
y = -4(-2)^2 + 5
y = -11
When x = 1,
y = -4(1)^2 + 5
y = 1
When x = 2,
y = -4(2)^2 + 5
y = -11
Plotting these 5 points, we connect a smooth curve.
Shown below:
Help Please! Will give brainliest and 45 points!
What is 12/10 as a decimal? What is 132/100 as a decimal? What is 546/100 as a decimal? What is 123/10 as a decimal? What is 872/100 as a decimal?
Answer:
That's literally all there is to it! 12/100 as a decimal is 0.12. I wish I had more to tell you about converting a fraction into a decimal but it really is that simple and there's nothing more to say about it. If you want to practice, grab yourself a pen and a pad and try to calculate some fractions to decimal format yourself.
Step-by-step explanation:
Happy 2 help :)
Answer:
12/10 = 1.2132/100 = 1.32 546/100 = 5.46123/10 = 12.3 872/100 = 8.72Step-by-step explanation:
1) 12/10 as a decimal is?
→ 12/10
→ 6/5 = 1.2
2) 132/100 as a decimal is?
→ 132/100
→ 1.32
3) 546/100 as a decimal is?
→ 546/100
→ 5.46
4) 123/10 as a decimal is?
→ 123/10
→ 12.3
5) 872/100 as a decimal is?
→ 872/100
→ 8.72
Hence, these are the answers.
Choose either Yes or No to tell whether there is an angle of the given measure shown in the diagram.
The addition of all angles in the diagram is equal to 360 degrees. Let's call angle x to the unknown angle. Then, we have:
[tex]\begin{gathered} m\angle x+160\degree+40\degree+65\degree+25\degree=360\degree \\ m\angle x=360\degree-160\degree-40\degree-65\degree-25\degree \\ m\angle x=70\degree \end{gathered}[/tex]Therefore, there is an angle that measures 70°.
Combining the angles of 160°, 40°, and 65°, we get a new angle, let's call it y, that measures:
[tex]\begin{gathered} m\angle y=160\degree+40\degree+65\degree \\ m\angle y=265\degree \end{gathered}[/tex]Therefore, there is an angle that measures 265°.
Combining the angles of 160°, 70°, 25°, and 65°, we get a new angle, let's call it z, that measures:
[tex]\begin{gathered} m\angle z=160\degree+70\degree+25\degree+65\degree \\ m\angle z=320\degree \end{gathered}[/tex]Therefore, there is an angle that measures 320°.
Combining the angles of 25°, and 65°, we get a new angle, let's call it a, that measures:
[tex]\begin{gathered} m\angle a=25\degree+65\degree \\ m\angle a=90\degree \end{gathered}[/tex]Therefore, there is an angle that measures 90°.
On the other hand, there is no combination of angles that add up to 225°
Chapter 3: Linear Functions - HomeworkScore: 65/100 12/18 answeredQuestion 11<>Linear ApplicationThe function E(t) = 3863 77.8t gives the surface elevation (in feet above sea level) of LakePowell t years after 1999.Pr
The given function is:
[tex]E(t)=3863-77.8t[/tex]This function is written in the form:
[tex]y=b+mx[/tex]Where b is the y-intercept, and m is the slope of the function. In this case, b=3863 and m=-77.8
The slope is negative, it means the function is decreasing, and the rate of decreasing is the value of the slope, so:
The surface elevation of Lake Power is decreasing at a rate of 77.8 ft/year
F(x)=15x+25 find f(1/5)
Given the function:
[tex]f(x)=15x+25[/tex]You need to substitute the following value of "x" into the function:
[tex]x=\frac{1}{5}[/tex]And then evaluate, in order to find:
[tex]f(\frac{1}{5})[/tex]Therefore, you get:
[tex]f(\frac{1}{5})=15(\frac{1}{5})+25[/tex][tex]f(\frac{1}{5})=\frac{15}{5}+25[/tex][tex]\begin{gathered} f(\frac{1}{5})=3+25 \\ \\ f(\frac{1}{5})=28 \end{gathered}[/tex]Hence, the answer is:
[tex]f(\frac{1}{5})=28[/tex]Kendra has not completed [tex] \frac{1}{5} [/tex]of the experiment for her science fair project she plans to work on her project over the next few weeks she would like to complete [tex] \frac{1}{4} [/tex]of the remaining experiment next week what fraction of the original experiment will she complete next week
We know that Kendra has not completed 1/5 of the project. To find 1/4 of the remaining part, we just have to multiply.
[tex]\frac{1}{4}\cdot\frac{1}{5}=\frac{1}{20}[/tex]Observe that 1/5 is the remaining part because it's the fraction that represents the not completed part.
Hence, she will complete the 1/20 of the project next week.Mrs. Gomez has two kinds of flowers in her garden. The ratio of lillies to daisies is the garden is 5:2 If there are 20 lillies, what is the total number of flowers in her garden? If there are 20 lillies, what is the total number of flowers in her garden?A. 8B. 10C. 15D. 28
The ratio of lilies to daisies is the garden is 5:2
20 Lillies
That means per every 4 lilies there are 2 daisies
4* 5 = 20 lilies
So
2*4 = 8 daisies
_________________
total number of flower are 20 lillies + 8 daisies = 28.
____________________________________
Answer
Option D) 28
solve the following equation y^4+7y^2-44=0
Answer:
y = 2, y = -2, y = i √11, y = - i √ 11
Explanation:
To solve the equation for y, we first make the substitution x = y^2. Doing this we write
[tex]x^2+7x-44=0[/tex]The above can be written as
[tex](x-4)(x+11)=0[/tex]Which gives two equations
[tex]\begin{gathered} x-4=0 \\ x+11=0 \end{gathered}[/tex]Substituting back x = y^2 gives
[tex]\begin{gathered} y^2-4=0\rightarrow y=-2,y=2 \\ x^2+11=0\rightarrow y=i\sqrt[]{11},y=-i\sqrt[]{11} \end{gathered}[/tex]Hence, to summarize, the solution to the equation is
[tex]\begin{gathered} y=-2,y=2 \\ y=i\sqrt[]{11},y=-i\sqrt[]{11} \end{gathered}[/tex]cit Formula = 18 + 7(58 - 1) 58 CRIBE EN ORACIONES COMPLETAS
a. As you can see, the sequence starts at -3, and increases by 7 each time, Amanda is wrong because she found the following formula:
an = 18 + 7(n - 1)
For n =1 the result should be -3:
n = 1
a1 = 18 + 7(1 - 1) = 18 + 7(0) = 18 + 0 = 18, she miscalculated the first term, and the whole sequence in general.
b. A possible sequence identification could be:
an = 7n - 10
Let's verify it:
n=1
a1 = 7(1) - 10 = 7 - 10 = -3
n=2
a2 = 7(2) - 10 = 14 - 10 = 4
n=3
a3 = 7(3) - 10 = 21 - 10 = 11
and so on...
Now for n=58
a58 = 7(58) - 10 = 396
-------------------------------------------------------------------------
32 = 2 + 3(n - 1)
Solving for n:
Use distributive property on the right hand side:
32 = 2 + 3n - 3
32 = 3n - 1
Add 1 to both sides:
32 +1 = 3n - 1 + 1
33 = 3n
Divide both sides by 3:
33/3 = 3n/3
11 = n
n = 11
If _____________, then the graph of the polynomial function is symmetric about the origin.f(x) = -f(-x)f(x) = -f(x)f(x) = f(-x)f(x) = f(x + 1)
ANSWER:
1st option: f(x) = -f(-x)
STEP-BY-STEP EXPLANATION:
The polynomial function is symmetric about the origin in the odds functions, where the following is true:
[tex]\begin{gathered} f(-x)=-f(x) \\ \\ \text{ Therefore:} \\ \\ f(x)=-f(-x) \end{gathered}[/tex]Then it would be:
If f(x) = -f(-x), then the graph of the polynomial function is symmetric about the origin.
The correct answer is the 1st option: f(x) = -f(-x)
In a poll, 50 residents in Greenville and Fairfield were asked whether they prefer swimming or jogging for exercise. This table shows the relative frequencies from the survey.The graph is in the pictureBased on the data in the table, which statements are true? Select all that apply.
Looking at the relative frequencies of the data in the table, these statements are true - "Greenville residents prefer jogging over swimming", "Fairfield residents prefer swimming over jogging", "People who prefer swimming are more likely to be from Fairfield", "People who prefer jogging are more likely to be from Greenville", "There is an association between the town a person lives in and their exercise preference".
It is given to us that -
50 residents in Greenville and Fairfield were asked whether they prefer swimming or jogging for exercise
The given table shows the relative frequencies from the survey.
We have to find out all the statements that are true about this survey.
Greenville people that like swimming = 0.18Greenville people that like jogging = 0.38=> Most Greenville residents prefer jogging over swimming
Similarly, we can see that
Fairfield residents prefer swimming over jogging (0.24>0.20)It can also be said true about the statements that -
People who prefer swimming are more likely to be from FairfieldPeople who prefer jogging are more likely to be from GreenvilleSince more people from Greenville prefers jogging to swimming and more people people from Fairfield prefers swimming to jogging, therefore "There is an association between the town a person lives in and their exercise preference"
Thus, according to the relative frequencies these statements are true - "Greenville residents prefer jogging over swimming", "Fairfield residents prefer swimming over jogging", "People who prefer swimming are more likely to be from Fairfield", "People who prefer jogging are more likely to be from Greenville", "There is an association between the town a person lives in and their exercise preference".
To learn more about relative frequencies visit
https://brainly.com/question/16832475
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This relation map is a student to the English class they are taking… Is this relation a function
Remember that
The data set is a function, if every element of the domain corresponds to exactly one element of the range
In this problem
the element of the domain Andy Rogers, has two different values of the English Class (element of the range)
that means
Is not a function
the answer is No1) What angle relationship/relationships do you see in the below diagram that would help you solve for the missing angle measurements? 2) Write an equation and solve for the measurements of Angle RQS & Angle UQT
The relationship is that the sum of all the angles is 360 degrees.
Because they are angles around a point.
Therefore,
3x + 90 + 4x + 221 = 360
3x+4x+90+221=360
7x+311=360
7x=360-311=49
Hence
x = 49 / 7 =7
Angle RQS = 3x = 3(7) =21 degrees
Angle RQS = 21 degrees
Angle UQT = 4x = 4(7) = 28 degrees
Angle UQT = 28 degrees
the question i have says “which statement correctly compares the rates of change of the two functions” and i dont understand how to solve it
The rate of change of function A is 4
The rate of change of function B is 3 (option D)
Explanation:We are looking for the rate of change of two functions.
m is also known as the rate of change
[tex]\begin{gathered} \text{Function A is given as:} \\ y\text{ = 4x + 6} \end{gathered}[/tex]comparing the equation above to a linear function:
y = mx + b
m = slope , b = y -intercept
For function A:
m = slope = 4, b = 6
To get the rate of change of function B, we need to find the slope of any two points on the table.
For linear function, the slope is constant irrespective of the two points used in calculating it.
Formula for slope:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]using points; (1, 3) and (3, 9)
[tex]\begin{gathered} x_1=1,y_1=3,x_2=3,y_2\text{ = 9} \\ \text{slope = }\frac{9-3}{3-1} \\ \text{slope = }\frac{6}{2} \\ \text{slope = 3} \\ \text{Slope for function B is 3} \end{gathered}[/tex]The rate of change of function A is 4
The rate of change of function B is 3 (option D)